{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T14:29:54Z","timestamp":1774967394915,"version":"3.50.1"},"reference-count":21,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,19]],"date-time":"2022-02-19T00:00:00Z","timestamp":1645228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A symmetry-based hybrid precoder and combiner is a high spectral efficiency structure in millimeter-wave (mmWave) massive multiple-input multiple-output (mMIMO) non-orthogonal multiple access (NOMA) system. To improve the spectral efficiency of the mmWave mMIMO-NOMA system, we first propose a user grouping scheme to suppress the strong inter-user interference caused by NOMA, then the hybrid precoder based on user channel alignment and the zero-forcing algorithm is constructed to further improve the signal-to-interference-plus-noise ratio (SINR) of the receiver. Subsequently, the non-convex spectral efficiency optimization problem is transformed into a convex optimization problem of inter-cluster power allocation and the closed-form solution for the optimal power under the minimum rate constraint is obtained by solving the KKT condition to further improve the spectral efficiency. The simulation results show that the proposed scheme can achieve higher spectral efficiency compared to orthogonal multiple access (OMA), fixed power allocation (FPA), K-means, and cluster head selection (CHS).<\/jats:p>","DOI":"10.3390\/sym14020412","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T08:34:47Z","timestamp":1645432487000},"page":"412","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Hybrid Precoding-Based Millimeter Wave Massive MIMO-NOMA Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4239-3749","authenticated-orcid":false,"given":"Zaoxing","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Honggui","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuxin","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"},{"name":"College of Information Science and Engineering, Changsha Normal University, Teli Road, Changsha 410100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinhao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Lushan South Road, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1109\/OJCOMS.2020.3010270","article-title":"6G Wireless Communication Systems: Applications, Requirements, Technologies, Challenges, and Research Directions","volume":"1","author":"Chowdhury","year":"2020","journal-title":"IEEE Open J. Commun. Soc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"57726","DOI":"10.1109\/ACCESS.2021.3071992","article-title":"User Clustering and Optimized Power Allocation for D2D Communications at mmWave Underlaying MIMO-NOMA Cellular Networks","volume":"9","author":"Solaiman","year":"2021","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1109\/JSTSP.2019.2922821","article-title":"Cluster Grouping and Power Control For Angle-Domain MmWave MIMO NOMA Systems","volume":"13","author":"Hu","year":"2019","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4421","DOI":"10.1109\/JSYST.2020.3015766","article-title":"A Two-Stage Power Allocation-Based NOMA Architecture for Optical Camera Communication","volume":"15","author":"Shahjalal","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"62367","DOI":"10.1109\/ACCESS.2020.2984204","article-title":"A Comprehensive Survey on Millimeter Wave Communications for Fifth-Generation Wireless Networks: Feasibility and Challenges","volume":"8","author":"Uwaechia","year":"2020","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2294","DOI":"10.1109\/TCOMM.2018.2883079","article-title":"Joint Beamforming and Jamming Optimization for Secure Transmission in MISO-NOMA Networks","volume":"67","author":"Zhao","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5114","DOI":"10.1109\/TCOMM.2019.2906589","article-title":"Joint Tx-Rx Beamforming and Power Allocation for 5G Millimeter-Wave Non-Orthogonal Multiple Access Networks","volume":"67","author":"Zhu","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2370","DOI":"10.1109\/JSAC.2017.2725878","article-title":"Spectrum and Energy-Efficient Beamspace MIMO-NOMA for Millimeter-Wave Communications Using Lens Antenna Array","volume":"35","author":"Wang","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5065","DOI":"10.1109\/TWC.2019.2932070","article-title":"Millimeter-Wave NOMA With User Grouping, Power Allocation and Hybrid Beamforming","volume":"18","author":"Zhu","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Xiong, C., Hua, Z., Lv, K., and Li, X. (2016, January 16\u201318). An Improved K-means Text Clustering Algorithm by Optimizing Initial Cluster Centers. Proceedings of the 2016 7th International Conference on Cloud Computing and Big Data (CCBD), Macau, China.","DOI":"10.1109\/CCBD.2016.059"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/JSAC.2018.2872364","article-title":"Hybrid Precoding-Based Millimeter-Wave Massive MIMO-NOMA With Simultaneous Wireless Information and Power Transfer","volume":"37","author":"Dai","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1109\/LWC.2017.2741493","article-title":"Energy-Efficient Power Allocation in Millimeter Wave Massive MIMO With Non-Orthogonal Multiple Access","volume":"6","author":"Hao","year":"2017","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhu, J., Li, Q., Liu, Z., Chen, H., and Vincent Poor, H. (2021). Enhanced User Grouping and Power Allocation for Hybrid mmWave MIMO-NOMA systems. IEEE Trans. Wirel. Commun., 1.","DOI":"10.1109\/TWC.2021.3109053"},{"key":"ref_14","first-page":"2744","article-title":"On Optimal Power Allocation for Downlink Non-Orthogonal Multiple Access Systems","volume":"35","author":"Zhu","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rezvani, S., Jorswieck, E.A., Joda, R., and Yanikomeroglu, H. (2022). Optimal Power Allocation in Downlink Multicarrier NOMA Systems: Theory and Fast Algorithms. IEEE J. Sel. Areas Commun., 1.","DOI":"10.1109\/JSAC.2022.3143237"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2961","DOI":"10.1109\/TWC.2018.2804953","article-title":"Joint Power Allocation and Beamforming for Non-Orthogonal Multiple Access (NOMA) in 5G Millimeter Wave Communications","volume":"17","author":"Xiao","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5465","DOI":"10.1109\/TWC.2018.2844207","article-title":"Hybrid Precoding Architecture for Massive Multiuser MIMO With Dissipation: Sub-Connected or Fully Connected Structures?","volume":"17","author":"Du","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1109\/JSTSP.2016.2523924","article-title":"An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems","volume":"10","author":"Heath","year":"2016","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/TSP.2014.2370947","article-title":"A Hybrid RF\/Baseband Precoding Processor Based on Parallel-Index-Selection Matrix-Inversion-Bypass Simultaneous Orthogonal Matching Pursuit for Millimeter Wave MIMO Systems","volume":"63","author":"Lee","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1109\/TWC.2014.011714.130846","article-title":"Spatially Sparse Precoding in Millimeter Wave MIMO Systems","volume":"13","author":"Ayach","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Rezvani, S., Jorswieck, E.A., Mokari, N., and Javan, M.R. (2021). Optimal SIC Ordering and Power Allocation in Downlink Multi-Cell NOMA Systems. IEEE Trans. Wirel. Commun., 1.","DOI":"10.1109\/ICC42927.2021.9500757"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/412\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:22:58Z","timestamp":1760134978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/2\/412"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,19]]},"references-count":21,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["sym14020412"],"URL":"https:\/\/doi.org\/10.3390\/sym14020412","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,19]]}}}